To proceed further, we need to define more properly the dyadic Green function above. We will skip the derivation, which can be found elsewhere [1]}, [2]}, [3]}, [4]}. In translationally-invariant and isotropic media, the dyadic Green function \({\bf G}_\text{b}({\bf r},{\bf r}^{\prime }) \equiv {\bf G}_\text{b}({\bf r}-{\bf r}^{\prime })\)  in Cartesian coordinates is given by
\({\bf G}_\text{b}({\bf r}-{\bf r}^{\prime }) = - \frac{\delta ({\bf R})}{3k_\text{b}^2} {\bf I}+ \text{PV} \left\lbrace \frac{\exp [i k_\text{b}R]}{4\pi R} \left[ {\bf I}- {\bf u}\otimes {\bf u}+ \frac{i k_\text{b}R-1}{(k_\text{b}R)^2} \left( {\bf I}- 3 {\bf u}\otimes {\bf u}\right) \right] \right\rbrace , \nonumber \\\) 
